Heat oven to 375°. Mix sugar, egg and shortening thoroughly. Stir in milk. Blend in flour, baking powder and salt. Melt butter. Sprinkle as much cinnamon over brown sugar as you wish.
Halve and pit apricots. Place rounded side up in rows of four. You may need fewer or more apricots, depending on their size. Spread cake mixture over apricots.
Bake 25-35 minutes. When done place a plate over pan and flip cake out of pan. Place a walnut half in each apricot cup. Serve warm.